Hadron Spectroscopy Lecture 1 Introduction and Motivation

Transcription

1 Hadron Spectroscopy Lecture 1 Introduction and Motivation National Nuclear Physics Summer School at MIT Matthew Shepherd Indiana University

2 Outline 1. Overview and Motivation 1.1.Uniue features of QCD 1.2. Why use spectroscopy as a tool to study QCD? 1.3. How do we classify mesons? 1.4. Introduction to experiment 2. Spectroscopy of Heavy Quark Systems 3. Spectroscopy of Light Quark Systems 4. Summary and Outlook: Present and Future Facilities 2

3 QCD in the Standard Model Three uark colors Color singlets apparently reuired Two typical arrangements: mesons and baryons Mesons (e.g., π, K, D) Fundamental Particles Q ua r ks L e pt o n s uup ddown c charm s strange ttop b bottom ν e ν µ ν τ electron neutrino e muon neutrino tau neutrino µ τ g W Z γ G au g e B os electron muon tau o n s Baryons (e.g., proton and neutron) Matter Constituents Higgs Boson Force Mediators 3

4 Evidence of Color ++ B(B 0! D 0 0 )= D 0 B 0 0 u u u J = 3 2 B(B 0! D + )= B 0 4 D

5 More Evidence of 3 Colors R J/ψ ψ Mark-I Mark-I + LGW Mark-II PLUTO DASP Crystal Ball BES ψ 3770 ψ 4040 ψ 4160 ψ E [GeV] Probes the ratio of uark to lepton couplings in QED: Q 2 / Qµ 2 e - R = e + e e - µ - µ + Homework: Compute the expected value of R below and above charm (and bottom) thresholds under the assumptions that there are 1 and 3 colors of uarks. Compare with experimental data from the PDG. 5

6 Interactions in QED Have: freely propagating spin-1/2 particle Want: physics to remain invariant under local phase transformations L = i(~c) µ (mc 2 )! e i (x) Doing so reuires introduction of a freely propagating massless gauge field (the photon) and the interaction of this field with spin-1/2 particles 1 16 F µ F µ Q( µ )A µ 6

7 Interactions in QCD Have: freely propagating spin-1/2 uark in rgb space Want: physics to remain invariant under unitary color transformations L = i(~c) µ (mc 2 r g b A! r g b A This reuires the introduction of eight massless gauge fields (the gluons) and several interaction terms -- note that gluons interact with each other! gluons uark-gluon vertex three-gluon vertex four-gluon vertex 7

8 Higher Order Corrections In QED, vacuum polarization acts to screen the charges of interacting particles resulting in weaker force at large distance. scale of corrections set by α = 1/137 In QCD uark loops continue to screen the QCD force, but gluon loops provide an anti-screening effect that dominates, resulting in a stronger force at large distances. scale of QCD corrections set by αs > 0.1 8

9 The Forces that Bind Hydrogen and Mesons The Electromagnetic Force and Quantum Electrodynamics (QED) (Hydrogen Atom) Simple Term e photon p The Strong Force and Quantum Chromodynamics (QCD) (Meson) gluon Simple Term (small distances) e Correction e e + p Correction (large distances) Potential V ( r) = r Potential (model) 4 3 r ( r) = s + F r V 0 IONIZATION IS POSSIBLE QUARKS ARE CONFINED 9

10 Gluon Interactions in QCD S. Bethke hep-ex/ QCD has interesting properties gluon-gluon interactions confinement Nonpurturbative in the interesting domain Study QCD using hadrons 10

11 Studying Forces with Spectroscopy Electromagnetic Force Strong Force c c Hydrogen Charmonium 11

12 Spectroscopy and QCD Studying the spectrum of hadrons motivated the uark model and led to development of QCD QCD has interesting properties confinement: force is strong at large distances color neutral hadrons, which can be made with any number of uarks gluon-gluon interactions How do these properties exhibit themselves in experimental data? Why is the spectrum of hadrons observed in nature so simple? Same fundamental uestions exist for mesons and baryons. Our discussion will focus on mesons. 12

13 Other Uniue States of Matter d u g c c g g Not forbidden by QCD - do they exist? 13

14 Classifying Mesons

15 Properties of Mesons mass width or lifetime total angular momentum parity charge conjugation charge and isospin 15

16 Constituent Quark Model Assemble mesons from spin 1/2 constituent uarks with effective masses a model: not the uark fields in the QCD Lagrangian Fundamental Pa 177 GeV 1.5 GeV (unstable) Q ua few hundred MeV r ks L uup ddown c charm s strange ttop b bottom 0.5 GeV 4.7 GeV 16

17 J PC color singlet uark anti-uark P: inverts coordinates uark wave function is odd under spatial inversion for L odd: (-1) L Intrinsic party of uark anti-uark: 1 x -1 = -1 C: particle anti-particle neutral eigenstates J = L + S P = (-1) L+1 C = (-1) L+S spatial inversion: (-1)L fermion anti-fermion: -1 S = 0 or 1, and L = 0, 1, 2, opposite spins: -1S+1 17

18 Charmonium Spectrum All states below 2 M D observed No extra states below 2 M D Good agreement with potential model calculation No missing states - no extra states 18

19 Isospin symmetry from mu md in isospin space: u has I = 1/2, Iz = 1/2 d has I = 1/2, Iz = -1/2 Combining uark antiuark elements from this vector space gives four combinations (examples for 0 -+ given) u di! + 1 p 2 uūi d di! 0 1 dūi! Homework: why are these almost exactly a factor of 2 different? B( (2S)! + J/ ) =0.34 B( (2S)! 0 0 J/ ) =0.18 Homework: why is the first so much bigger than the second even though there is less phase space available? p2 B( (2S)! J/ ) =0.034 B( (2S)! 0 J/ ) = uūi + d di! triplet: isovector (I = 1) singlet: isoscalar (I = 0) 19

20 G Parity Extension of C to isovectors (charged particles): apply C rotate by π in isospin space: u d Multiplicative Mostly conserved in strong interactions general: G = C(-1) I B( 0! + ) 1 B( 0! + 0 )= u di! ūdi! dui isospin: 0 : G = C uūi + d di! d di + uūi isospin: 1 : G = -C uūi d di! d di uūi B(!! + )=0.015 B(!! + 0 )=

21 Light Quark Nonets strangeness strangeness K 0 K + K* 0 K* + π - η π 0 π + ρ - φ ρ 0 ρ + η isospin (z comp.) ω isospin (z comp.) K - K 0 K* - K* nonet neutrals: C=+ 1 - nonet neutrals: C=- 21

22 Meson Spectrum from Lattice QCD Dudek, Edwards, Guo, and Thomas, PRD 88, (2013) 3000 negative parity positive parity exotic lightest hybrids 500 All states have strangeness = 0 22

23 Hybrid Mesons color singlet uark anti-uark gluonic contribution (J PC )g = 1 +- mass GeV color-octet pair g J = L + S P = (-1) L+1 C = (-1) L+S Allowed J PC : 0 -+, 0 ++, 1 - -, 1 +-, 2 ++, Forbidden J PC : 0 - -, 0 +-, 1 -+, 2 +-, Lightest Hybrids S = 1 S = 0 J PC : 0 -+, 1 -+, exotic hybrid

24 Recap Know how to classify and sort mesons Enables identification of states that don t fit a pattern New patterns suggest new degrees of freedom QCD predicts new states that should not fit the standard pattern How do we produce them? How do we detect them? How do we measure the properties of mesons that we want to use to sort the spectrum? 24

25 Some Experimental Preliminaries

26 Meson Spectrum from Lattice QCD Dudek, Edwards, Guo, and Thomas, PRD 88, (2013) 3000 negative parity positive parity exotic lightest hybrids 500 All states have strangeness = 0 26

27 Decays and Conservation Laws Conservation laws that apply to all decays angular momentum four-momentum charge Symmetries/conservations laws of strong interactions C P isospin (mostly) uark flavor: strangeness or charmness Measuring these properties for decay products directly informs us of the properties of the parent particle 27

28 Production and Detection Colliding Beam e + e - proton-proton proton-antiproton Fixed Target electromagnetic or hadron beams SC Quadrupole Pylon Solenoid Coil Barrel Calorimeter Ring Imaging Cherenkov Detector Drift Chamber Inner Drift Chamber / Beampipe GlueX target start counter barrel calorimeter time-of -flight forward calorimeter SC Quadrupoles Rare Earth Quadrupole CLEO-c Magnet Iron Barrel Muon Chambers Endcap Calorimeter Iron Polepiece diamond wafer electron beam tagger magnet photon beam tagger to detector distance is not to scale electron beam central drift chamber superconducting magnet forward drift chambers 28

29 Detection: Observables Long lived particles charged: p, π, K neutral: n, γ, KL Types of detectors: tracking: measure momentum SC Quadrupole Pylon Solenoid Coil Barrel Calorimeter CLEO-c Ring Imaging Cherenkov Detector Drift Chamber Inner Drift Chamber / Beampipe calorimetry: measure energy particle ID: measure velocity Assemble pieces to get fourmomentum SC Quadrupoles Rare Earth Quadrupole Magnet Iron Barrel Muon Chambers Endcap Calorimeter Iron Polepiece 29

30 Histograms: Invariant Mass p! X Candidates per Bin reconstruct all particles consider all combinations of two photons γγ Invariant Mass [GeV/c ] p 0! gg 30

31 Branching Fractions and Widths Experimentally accessible: B i = Theoretically interesting: Candidates per Bin i tot i / M i 2 (phase space) 160 resolution: 140 detector effect ( 0 )=8eV γγ Invariant Mass [GeV/c ] 31 ) 2 Entries/(5MeV/c N Data -N Fit N Data physics induced: χc0 is more likely to decay Data Global fit Background M(pnπ - π ) (GeV/c ) ( c0 ) = 10 MeV ( c1 )=0.8 MeV ( c2 )=1.9 MeV PRD 86,

32 Decays: The OZI Rule (S. Okubo, G. Zweig, and J. Iizuka) OZI Favored OZI Suppressed B(! KK)=0.83 B(! + 0 )=0.15 Helps one infer hidden uark flavor of mesons. 32

33 OZI Rule and Widths R J/ψ ψ Mark-I Mark-I + LGW Mark-II PLUTO DASP Crystal Ball BES ψ 3770 ψ 4040 ψ 4160 ψ E [GeV] c D c u c 33 c u D

34 Dalitz Plots Ds + K + K - π + PRD 83, spinless particle 3 spinless particles: X M X 2 = M M M13 2 for an X, dynamics is a function of two variables: M12 and M23 All information about decay can be learned by studying a Dalitz plot of M12 2 vs. M23 2 m 2 (K - π + ) (GeV 2 /c 4 ) Φ K + K - π + (b) K* K - π + phase space is uniform on this plot m 2 (K + K - ) (GeV 2 /c 4 )

35 Dalitz Plots Ds + K + K - π + Homework: the decay of a spinless particle to 3 spinless particles can be described by 3 x 4-vectors = 12 numbers. Use symmetry arguments and conservation laws to show that 10 of the 12 unknowns can be eliminated leaving only two remaining variables to describe the physics of the decay. m 2 (K - π + ) (GeV 2 /c 4 ) Φ K + K - π + PRD 83, (b) K* K - π + Any two variables will work, the Dalitz plot is a common choice m 2 (K + K - ) (GeV 2 /c 4 )

36 Experimental Strategy Search for new particles bumps in invariant mass spectra uniue decay patterns in phase space (more later) Measure mass and width decay modes uantum numbers: J PC Use to test predictions of the hadron spectrum from models or direct calculations of QCD 36